Introduction

Crucial to all good statistical analyses is a thorough exploratory analysis. In this document, we will introduce a few techniques for developing an understanding of our dataset, including an understanding of its limitations.

Load packages

Let’s load all the required R packages. See our tutorial 0_Installing_packages.html for installation information.

library(rgeos)
library(rgdal)
library(sp)
library(maptools)
library(spatstat)
library(spdep)
library(INLA)
library(inlabru)
library(readxl)
library(lubridate)
library(ggmap)
library(raster)

File set up

If you have not done so already, you need to download the two sets of files associated with the workshop.

All the workshop script and tutorial files can be found on Github at github.com/joenomiddlename/DFO_SDM_Workshop_2020. To download these files on your computer, press on Code and then Download ZIP. Once downloaded, unzip the DFO_SDM_Workshop_2020-main.zip file. To be able to access some of the precompiled data, we need to make the unzipped folder the working directory. To do so in R Studio, navigate to the correct folder using the bottom right panel (folder view, you can use button) and open it. Then, click “Set as Working Directory” under the tab ‘More’.

We should be inside the folder titled: ‘DFO_SDM_Workshop_2020’, you can verify this by using getwd().

Now we can load in the precompiled data

list2env(readRDS('./Data/Compiled_Data_new.rds'), globalenv())
## <environment: R_GlobalEnv>

Fin whale data

Throughout this workshop, we use data collected on fin whales in June, July, and August across the years 2007-2009 and for 2011. There are two main types of data:

  • Encounters from systematic aerial surveys, found in Sightings_survey. The encounters information contain counts of fin whales, although for this tutorial we simplify the analysis and only model presence/absence. These systematic surveys also contain information on the distance of the encounters from the plane. Furthermore, they are accompanied with the aerial tracklines, found in Effort_survey. In these data objects, we combined three surveys conducted by both DFO and NOAA: 2007 T-NASS Aerial Survey (Lawson et al. 2009), NOAA NARW Surveys (Cole, NOAA), and NOAA Cetacean Surveys (Cole et al., NOAA).

  • Opportunistic fin whale encounters from two whale-watching operators, found in Sightings_DRWW_sp. This dataset is not accompanied by tracklines. Again, these datasets contains whale counts, but for simplicity we will analyze them as presence/absence data in these tutorials. These encounters are maintained in the DFO Maritimes Region Whale Sightings Database (MacDonald et. al. 2017).

  • Distance from port for both the Quoddy and Brier whale watch vessels, found in Dist_Brier and Dist_Quoddy. These covariates will be used to model effort from the whale watch vessels.

  • Bathymetric slope data, found in Slope. Slope data will be our main covariate in our analysis and we will explore whether the distribution of fin whales is linked to this.

Coordinate reference system

These data are spatially-referenced data. The first thing we must always do is check for consistency between the coordinate reference systems (CRS) of each spatial object in use! To print the CRS of an sp object, simply add @proj4string to the name of the spatial object and run.

Sightings_DRWW_sp@proj4string 
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
Sightings_survey@proj4string 
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
Effort_survey@proj4string 
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
Domain@proj4string 
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
Slope@proj4string
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
WW_ports@proj4string
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
Dist_Brier@proj4string
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs
Dist_Quoddy@proj4string
## CRS arguments: +proj=longlat +datum=WGS84 +no_defs

All of the spatial objects are in lat/lon - good! For future analysis we will be projecting the data into a different coordinate reference system to better preserve euclidean distance.

Finally, let’s turn off all warnings associated with coordinate reference systems. The latest PROJ6+/GDAL3+ updates have caused many warning messages to be printed.

rgdal::set_rgdal_show_exportToProj4_warnings(FALSE)
rgdal::set_thin_PROJ6_warnings(TRUE)
options("rgdal_show_exportToProj4_warnings"="none")

Plotting the data

Our first goal is generally to plot the data on a map. The gg() and gmap() functions from the inlabru package are extremely useful at plotting spatial data! The class of spatial objects we will use are from the sp package. The classes of these objects begin with ‘Spatial’. For example SpatialPointsDataFrame.

We have written a bespoke function gg.spatiallines_mod() to easily add SpatialLinesDataFrame objects to the plots too. This will prove useful for plotting transect lines. We load the bespoke functions to the working environment now.

source('utility_functions.R')

Let’s plot our data!

If the data are in lat/lon format then the gmap() function will automatically add a terrain layer to the plots. Let’s plot the survey encounters in blue, the survey tracklines in black, the whale-watch encounters in purple, the whale watch ports in red.

gmap(Sightings_survey) +
  gg(Domain) +
  gg.spatiallines_mod(Effort_survey) +
  gg(Sightings_survey, colour='blue') +
  gg(Sightings_DRWW_sp, colour='purple') +
  gg(WW_ports, colour='red')

Some of the maps used by default in gmap are copyrighted (e.g., Google maps, see ?get_map), see Additional tips for ways to use open-source maps for publication.

To remove the map layer, simply replace the gmap(Sightings_survey) with ggplot().

ggplot() + # Notice the empty ggplot() call
  gg(Domain) +
  gg.spatiallines_mod(Effort_survey) +
  gg(Sightings_survey, colour='blue') +
  gg(Sightings_DRWW_sp, colour='purple') +
  gg(WW_ports, colour='red')

This plot hides some crucial information regarding the data collection. For example, the survey encounters and tracklines do not come from a single survey, or even a single organisation! Let’s plot this! The easiest way to do this is to subset the data accordingly!

table(Effort_survey$DATASET)
## 
##    DFO NOAA_1 NOAA_2 
##     49     54     70
# there are 3 surveys
ggplot() +
  gg(Domain) +
  gg.spatiallines_mod(Effort_survey[Effort_survey$DATASET=='DFO',], colour='purple') +
  gg.spatiallines_mod(Effort_survey[Effort_survey$DATASET=='NOAA_1',], colour='red') +
  gg.spatiallines_mod(Effort_survey[Effort_survey$DATASET=='NOAA_2',], colour='yellow')

This is problematic! The DFO tracklines (in purple) do not overlap with the two NOAA surveys! Thus, any future model will be unable to identify any differences in protocol efficiency without strict assumptions. This is because any model intercepts will be confounded with the latent spatial field. More on this later!

Exercise 1

In addition, the surveys were conducted across 4 separate years. Let’s plot the survey tracklines by year. Do you see any cause for concern? Note that the names of the variables in the Effort_Survey are: DATASET and YEAR. Try this on your own! If you get stuck, click ‘Show Code’. Hint: The YEAR variable is of type character and contains 4 unique values (see below).

table(Effort_survey$YEAR)
## 
## 2007 2008 2009 2011 
##  101   20   19   33
class(Effort_survey$YEAR)
## [1] "character"
ggplot() +
  gg(Domain) +
  gg.spatiallines_mod(Effort_survey[Effort_survey$YEAR=='2007',], colour='purple') +
  gg.spatiallines_mod(Effort_survey[Effort_survey$YEAR=='2008',], colour='red') +
  gg.spatiallines_mod(Effort_survey[Effort_survey$YEAR=='2009',], colour='blue') +
  gg.spatiallines_mod(Effort_survey[Effort_survey$YEAR=='2011',], colour='yellow')

Note that the surveys from years 2007, 2008 and 2009 covered largely different regions! Again, this is problematic if we want to model any changes in the whale distribution over time! The effect of year will be confounded by the spatial field. That being said, the data from 2011 appear to be a good candidate for model comparison as the spatial range overlaps with the other 3 years’ effort. We will holdout this data as our test data and use 2007, 2008, and 2009 as our training data.

xtabs(~ YEAR + DATASET, data=Effort_survey@data)
##       DATASET
## YEAR   DFO NOAA_1 NOAA_2
##   2007  49      3     49
##   2008   0     20      0
##   2009   0     19      0
##   2011   0     12     21

2011’s data comes exclusively from NOAA.

Transforming the data into a new CRS

For modelling, we will transform the data from lat/lon into a new “Canadian” CRS: NAD83 datum with UTM Zone 20N projection. This projection will help to preserve euclidean distance between points. We define the CRS object for this projection with EPSG code 2961:

Can_proj <- CRS("+init=EPSG:2961")
Can_proj <- fm_crs_set_lengthunit(Can_proj, unit='km')

The second line of code specifies that we want to work in units of km instead of the default meters. This can prove vital in applications to avoid numerical overflow.

Transforming spatial points, lines, and polygons

To do the transformation, we will use the spTransform() function. For example, we transform the whale-watch encounters spatial object Sightings_DRWW_sp as follow:

Sightings_DRWW_sp <- spTransform(Sightings_DRWW_sp, Can_proj)
Sightings_DRWW_sp@proj4string
## CRS arguments:
##  +proj=tmerc +lat_0=0 +lon_0=-63 +k=0.9996 +x_0=500000 +y_0=0
## +ellps=GRS80 +units=km +no_defs

Notice the changed output from calling @proj4string.

Exercise 2

Please repeat this for all the spatial objects that are points, lines or polygons.

Sightings_survey <- spTransform(Sightings_survey, Can_proj)
Effort_survey <- spTransform(Effort_survey, Can_proj)
WW_ports <- spTransform(WW_ports, Can_proj)
Domain <- spTransform(Domain, Can_proj)

Transforming raster-like spatial pixels objects

Transforming the ‘raster’-like SpatialPixelsDataFrame objects (Slope, Dist_Brier, and Dist_Quoddy) using spTransform would be inappropriate here. The projection leads to a curvature of the pixels. A more appropriate approach here is to use bilinear interpolation. The projectRaster() function from the raster package works great for this. This requires converting the SpatialPixelsDataFrame object into an object of type raster. This is made easy with the function raster(). Finally, to convert the raster object back into a SpatialPixelsDataFrame, we can use the as() function from the maptools package. This function is extremely useful for converting spatial objects between the popular packages: sp, spatstat, raster, and sf. We use this function substantially throughout the workshop.

Slope <- as(projectRaster(raster(Slope), crs=Can_proj), 'SpatialPixelsDataFrame')
Dist_Brier <- as(projectRaster(raster(Dist_Brier), crs=Can_proj), 'SpatialPixelsDataFrame')
Dist_Quoddy <- as(projectRaster(raster(Dist_Quoddy), crs=Can_proj), 'SpatialPixelsDataFrame')

Plot the (transformed) Bathymetry and Distance from Port spatial objects. We are going to combine these into a single plot using the multiplot() function from the inlabru package. This function takes as input ggplot objects and an argument layout, specifying how the plots should be arranged (see Additional tips for ways to change the layout).

multiplot(ggplot() +
  gg(Domain) +
  gg(Slope) + xlab('East(km)') + ylab('North(km)') + labs(fill='Slope') + 
    coord_fixed(ratio = 1),
ggplot() +
  gg(Domain) +
  gg(Dist_Brier) + xlab('East(km)') + ylab('North(km)') + 
  coord_fixed(ratio = 1),
ggplot() +
  gg(Domain) +
  gg(Dist_Quoddy) + xlab('East(km)') + ylab('North(km)')+ 
  coord_fixed(ratio = 1),
layout=matrix(1:4, nrow=2, ncol=2, byrow = TRUE))

Don’t like the colour scheme? See Additional tips to learn how to define your own manually.

Simplifying the coastline (domain)

The Domain in its current form has a very complex coastline. In the second and third workshops, inlabru will require a triangulation mesh to be created that covers the Domain. Unfortunately, creating a triangulation mesh over a ‘wiggly’ coastline is very challenging and numerous issues can arise. For example, accurately capturing the ‘wigglyness’ of the coastline with a mesh requires it to have a large number of triangles, slowing down the computation. Conversely, failing to accurately capture the shape of the coastline can lead to some of the encounters to fall outside the mesh, forcing us to discard them!

To combat these issues, we will smooth the Domain using the functions gSimplify() and gBuffer(). gSimplify() attempts to reduce the number of segments used to define the SpatialPolygonsDataFrame. The amount of reduction is determined by the argument tol=. This should help to reduce the number of triangles required to recreate the coastline. Next, gBuffer() will extend (or buffer) the boundary of the SpatialPolygonsDataFrame by an amount determined by the argument width=. This should help to stop some of the encounters from falling outside of the mesh.

However, we should repeat the process once more for the covariates. inlabru requires that every covariate is defined at every point within the computational mesh. When the computational mesh is created later, the boundary may expand slightly. If the covariates are defined on the original domain, there may end up being points of the mesh that do not have a well-defined covariate value. To counter this, it can help to define a second extended and simplified domain for defining the covariates over. By ensuring that this second extended domain is slightly larger than the first extended domain, we can ensure that a covariate value is properly defined at every value in the computational mesh. We create these two domains below:

Domain_restricted <- gSimplify(gBuffer(Domain,width=15),tol=20)
# Plot
ggplot() +
  gg(Domain_restricted) +
  gg(Domain, color='red') +
  gg.spatiallines_mod(Effort_survey, color='blue')

# Does the new domain contain all the survey tracklines?
gContains(Domain_restricted,Effort_survey)
## [1] TRUE
# Create a new domain that is slightly larger - for defining covariates later
Domain_restricted2 <- gSimplify(gBuffer(Domain,width=35),tol=20)
# Plot
ggplot() +
  gg(Domain_restricted) +
  gg(Domain_restricted2, color='green') +
  gg(Domain, color='red')

# Does it contain the old 
gContains(Domain_restricted2,Domain_restricted)
## [1] TRUE

Great! We have defined two new buffered and smoothed domains. The original domain (Domain) is shown in red and is where the computation will take place. The domain over which the computational mesh will be defined (Domain_restricted) is shown in black. Lastly, the domain over which the covariates will be defined (Domain_restricted2) is shown in green.

Once again, the smoothing of the coastline helps us to define a computational mesh that has fewer numerical issues. All computations will still take place over the original domain (Domain). More on that later!

Extending the covariates to match the new domain

Now we must extend our covariates to take ‘sensible’ values at all points in Domain_restricted2. These imputed values will not affect the model estimates as the model will be fit to the original Domain.

Our covariate Slope is well-defined on the original (un-buffered) domain as defined by the SpatialPolygons Domain. At values outside this, we choose to ‘fill-in’ these points with nearest-neighbour imputations. Next, we redefine the covariate as a log Slope variable, which we call log_Slope. We take the logarithm to reduce the range of values the covariate can take as these could cause our models to make wild predictions in the future workshops. We discuss the reasons for taking a log transform in more depth later in this session.

## define log_slope covariate
log_Slope <- Slope
# Define all values on land equal to 0
#log_Depth$FIWH_MAR_Slope[log_Depth$FIWH_MAR_Slope >= 0] <- 0
log_Slope$FIWH_MAR_Slope <- log(log_Slope$FIWH_MAR_Slope)#log(1-log_Depth$FIWH_MAR_Slope)
names(log_Slope) <- 'log_Slope' 

# 1) Define a set of pixels across our modified domain
pixels_Domain <- as(SpatialPoints(makegrid(Domain_restricted2, n=100000),proj4string = Domain@proj4string),'SpatialPixels')[Domain_restricted2,]

# 2) Extract values of the covariate at the new pixel locations
pixels_Domain$log_Slope <- over(pixels_Domain,log_Slope)$log_Slope
# 3) impute missing values with the nearest neighbour value
pixels_Domain$log_Slope[is.na(pixels_Domain$log_Slope)] <- 
  log_Slope$log_Slope[nncross(as(SpatialPoints(pixels_Domain@coords[which(is.na(pixels_Domain$log_Slope)),]),
                                 'ppp'),as(SpatialPoints(log_Slope@coords),'ppp'), what = 'which')]
log_Slope <- pixels_Domain
# 4) Create a squared log depth covariate (for later)
log_Slope_sq <- log_Slope
names(log_Slope_sq) <- 'log_Slope_sq'
log_Slope_sq$log_Slope_sq <- log_Slope_sq$log_Slope_sq^2

# Plot the covariates with Domain_restricted overlayed
ggplot() + gg(log_Slope) + gg(Domain_restricted)

We also need to buffer and rescale the distance from port covariates Dist_Brier and Dist_Quoddy. Unlike with previous covariates, however, we will fix all buffered values on land equal to a large constant. This will help to ensure that negligible effort is recorded from the whale watch vessels on land through \(\lambda_{eff}\).

We show how to do it with the distance to Brier.

# 1) Define a set of pixels across our modified domain
pixels_Domain <- as(SpatialPoints(makegrid(Domain_restricted2, n=100000),proj4string = Domain@proj4string),'SpatialPixels')[Domain_restricted2,]

# Extract the average value of distance at the newly created pixel locations
pixels_Domain$Dist_Brier <- over(pixels_Domain,Dist_Brier)$Dist_Brier
# There are some missing values due to newly created pixels being on land
# Fill in missing values with a very large value (1000km).
# This will make the effect of these regions negligible on inference as lambda_eff will be small
pixels_Domain$Dist_Brier[is.na(pixels_Domain$Dist_Brier)] <- 1e3

Dist_Brier <- pixels_Domain

# There is an infinity value at the port. Change to 0
Dist_Brier$Dist_Brier[is.infinite(Dist_Brier$Dist_Brier)] <- 0
max(Dist_Brier$Dist_Brier)
## [1] 1000
# Let's scale the Dist covariates closer to the (0,1) scale
Dist_Brier$Dist_Brier <- Dist_Brier$Dist_Brier / 980.7996

ggplot() + gg(Dist_Brier) + gg(Domain)

Exercise

Now, please rescale and buffer the distance to Quoddy object.

pixels_Domain <- as(SpatialPoints(makegrid(Domain_restricted2, n=100000),proj4string = Domain@proj4string),'SpatialPixels')[Domain_restricted2,]

pixels_Domain$Dist_Quoddy <- over(pixels_Domain,Dist_Quoddy)$Dist_Quoddy
pixels_Domain$Dist_Quoddy[is.na(pixels_Domain$Dist_Quoddy)] <- 1e3

Dist_Quoddy <- pixels_Domain
# There is an infinity value at the port. Change to 0
Dist_Quoddy$Dist_Quoddy[is.infinite(Dist_Quoddy$Dist_Quoddy)] <- 0
# Let's scale the Dist covariates closer to the (0,1) scale
Dist_Quoddy$Dist_Quoddy <- Dist_Quoddy$Dist_Quoddy / 980.7996
ggplot() + gg(Dist_Quoddy) + gg(Domain)

Exploring detection function and effort layers of survey data

To explore which detection functions (\(p(d)\)) could be used with the survey data, we will first plot the histogram of measured distances from the plane (i.e. the observed distances of encounters from the trackline).

# What is the maximum detection distance?
ggplot(Sightings_survey@data, aes(x=DISTANCE)) + geom_histogram() + xlab('Distance (m)')

The histogram of the perpendicular distances from the aircraft shows an apparent maximum detection probability at a value of distance above 0 metres! Low detection probability close to 0 metres is common for aerial surveys since it is harder to see below the plane. Common approaches include truncating the data, and fitting a two-parameter distance sampling function that allows for a non-monotonic relationship to exist.

Given the limited size of the survey data and the scope of this workshop, we choose not to pursue either option and we instead continue with estimating a single-parameter detection probability function. This crude approach assumes the detection probability is a monotonically decreasing function of distance.

In addition, it is often advised in distance sampling applications to threshold our upper detection distances at a ‘sensible’ value. For the histogram above, it looks like 2km could be a reasonable threshold value to choose. Let’s set all values above 2km equal to 2km and scale the distances onto the km units scale. This rescaling to units of km is crucial for numerical stability. We define a variable ‘distance’ that contains the rescaled distances. Note that a few distances are missing. We impute these with the mean distance.

# Setting the distances <250 to 250
# Sightings_survey@data$DISTANCE <- ifelse(Sightings_survey@data$DISTANCE>250,Sightings_survey@data$DISTANCE,250)

# Setting the distances >2000 to 2000
Sightings_survey@data$DISTANCE <- 
  ifelse(Sightings_survey$DISTANCE>2000 & !is.na(Sightings_survey$DISTANCE),
         2000,Sightings_survey$DISTANCE)

# Needs renaming to match the formula argument
Sightings_survey$distance <- Sightings_survey$DISTANCE
# Impute missing distances with the mean
Sightings_survey$distance[is.na(Sightings_survey$distance)] <- mean(Sightings_survey$distance,na.rm=T)
# Remove the old DISTANCE column
Sightings_survey <- Sightings_survey[,-c(8)]
# Rescaling to km
Sightings_survey$distance <- Sightings_survey$distance / 1000

# Plot the modified distances
ggplot(Sightings_survey@data, aes(x=distance)) + geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

The single-parameter detection probability function we will use is the half-normal detection function:

\[p(d) = exp\left(\frac{-d^2}{2\sigma^2}\right)\]

Exploring covariates for effort in whale-watch data

In lecture 1 we showed how we could attempt to model effort with a set of informative covariates. This approach is most useful for opportunistic datasets which lack quality information on the observers’ locations. Throughout our tutorials, we will use distance from port as a covariate of effort for the the whale-watch data.

Here, we investigate a potential functional form for the distance from port covariate. To do this, we plot a histogram of the distances from port at each of the whale watch sighting locations.

# Plot the encounters with distance from the port
hist(over(Sightings_Brier_nodup,Dist_Brier)$Dist_Brier, main='Histogram of the distance from port of the Brier encounters', xlab = 'Distance from port')

hist(over(Sightings_Quoddy_nodup,Dist_Quoddy)$Dist_Quoddy,breaks=20, main='Histogram of the distance from port of the Quoddy encounters', xlab = 'Distance from port')

For both ports, we detect a decreasing frequency of encounters made as the distance from port increases. Based on the histograms, we choose to model the functional form as a half-normal function. More complicated functional forms (e.g. weibull or hazard functions) could also be used.

More specifically, let the whale-watch effort intensity from the \(i^{th}\) port be denoted \(\lambda_{eff, i}\) and let the location of the \(i^{th}\) port be denoted \(s_i^*\). Finally, let the scalar parameter \(\lambda_i\) be unique for each port. Then we assume the following functional form for the whale watch effort intensity from the \(i^{th}\) port: \[\lambda_{eff,i}(s) = \lambda_i exp\left(\frac{-||s-s_i^*||^2}{2\sigma_i^2} \right)\].

On the log scale, this covariate can be estimated as a linear effect on the squared distance from port. Thus, we create SpatialPixelsDataFrame objects which store the squared distances from port.

Dist_Brier_sq <- as(Dist_Brier,'SpatialPixels')
Dist_Brier_sq$Dist_Brier_sq <- Dist_Brier$Dist_Brier^2
Dist_Quoddy_sq <- as(Dist_Quoddy,'SpatialPixels')
Dist_Quoddy_sq$Dist_Quoddy_sq <- Dist_Quoddy$Dist_Quoddy^2

Exercises

If you got stuck on any of the exercises, then please feel free to try them again. Here are links to the problems:

  1. Plotting data by year

  2. Transforming spatial points and lines

Bonus Exercises

  1. Transform one of the spatial objects back into longitude latitude.
  2. Transform one of the spatial objects into units of meters.

Additional tips and code

Using OpenStreetMaps instead of Google Maps

For publication, there can be issues regarding copyright of Google Maps. Using OpenStreetMap can help. To guarantee this simply add the following argument: source='osm', force=TRUE to gmap(). Double check the console that the maps are indeed being downloaded from stamen or osm. For brevity we have suppressed the messages.

gmap(Sightings_survey, source='osm', force=TRUE) +
  gg(Domain) +
  gg.spatiallines_mod(Effort_survey) +
  gg(Sightings_survey, colour='blue') +
  gg(Sightings_DRWW_sp, colour='purple') +
  gg(WW_ports, colour='red')

Note for this to work it needs to be in the original project (lat/lon), not UTM.

The multiplot() function is a very flexible function that enables publication-quality figures to be made with relative ease.

Changing the layout of multiplot()

To change the order of the plots you can change the argument byrow=TRUE to byrow=FALSE.

multiplot(ggplot() +
  gg(Domain) +
  gg(Slope) + xlab('East(km)') + ylab('North(km)') + labs(fill='Slopeetry'),
ggplot() +
  gg(Domain) +
  gg(Dist_Brier) + xlab('East(km)') + ylab('North(km)'),
ggplot() +
  gg(Domain) +
  gg(Dist_Quoddy) + xlab('East(km)') + ylab('North(km)'),
layout=matrix(1:4, nrow=2, ncol=2, byrow = FALSE))

We can also change the size of the figures by changing the matrix in the layout.

multiplot(ggplot() +
  gg(Domain) +
  gg(Slope) + xlab('East(km)') + ylab('North(km)') + labs(fill='Slopeetry'),
ggplot() +
  gg(Domain) +
  gg(Dist_Brier) + xlab('East(km)') + ylab('North(km)'),
ggplot() +
  gg(Domain) +
  gg(Dist_Quoddy) + xlab('East(km)') + ylab('North(km)'),
layout=matrix(c(1,1,2,3), nrow=2, ncol=2, byrow = TRUE))

As you can see plots of different size stretches the maps, to keep the set projection we can use coord_fixed(ratio = 1).

multiplot(ggplot() +
  gg(Domain) +
  gg(Slope) + xlab('East(km)') + ylab('North(km)') + labs(fill='Slopeetry') +
    coord_fixed(ratio = 1),
ggplot() +
  gg(Domain) +
  gg(Dist_Brier) + xlab('East(km)') + ylab('North(km)') + 
  coord_fixed(ratio = 1),
ggplot() +
  gg(Domain) +
  gg(Dist_Quoddy) + xlab('East(km)') + ylab('North(km)') + 
  coord_fixed(ratio = 1),
layout=matrix(c(1,1,2,3), nrow=2, ncol=2, byrow = TRUE))

Define your own colour palette

We can define the colour palette easily.

colsc <- function(...) {
  scale_fill_gradientn(colours = rev(RColorBrewer::brewer.pal(11,"PuBuGn")),
                       limits = range(...))
}

Look at ?RColorBrewer::brewer.pal to see what other colour palettes are available.

multiplot(ggplot() +
  gg(Domain) +
  gg(Slope) + xlab('East(km)') + ylab('North(km)') + labs(fill='Slopeetry') +
  colsc(Slope@data[,1]),
ggplot() +
  gg(Domain) +
  gg(Dist_Brier) + xlab('East(km)') + ylab('North(km)') +
  colsc(Dist_Brier@data[,1]),
ggplot() +
  gg(Domain) +
  gg(Dist_Quoddy) + xlab('East(km)') + ylab('North(km)') +
  colsc(Dist_Quoddy@data[,1]),
layout=matrix(1:4, nrow=2, ncol=2, byrow = T))
## Warning in RColorBrewer::brewer.pal(11, "PuBuGn"): n too large, allowed maximum for palette PuBuGn is 9
## Returning the palette you asked for with that many colors

## Warning in RColorBrewer::brewer.pal(11, "PuBuGn"): n too large, allowed maximum for palette PuBuGn is 9
## Returning the palette you asked for with that many colors

## Warning in RColorBrewer::brewer.pal(11, "PuBuGn"): n too large, allowed maximum for palette PuBuGn is 9
## Returning the palette you asked for with that many colors

Have a go at creating your own colour palette function. Investigate the effects of changing both arguments to brewer.pal.

colsc2 <- function(...){
  scale_fill_gradientn(colours = rev(RColorBrewer::brewer.pal(7,"Spectral")),
                       limits = range(...))
}
multiplot(ggplot() +
  gg(Domain) +
  gg(Slope) + xlab('East(km)') + ylab('North(km)') + labs(fill='Slopeetry') +
  colsc2(Slope@data[,1]),
ggplot() +
  gg(Domain) +
  gg(Dist_Brier) + xlab('East(km)') + ylab('North(km)') +
  colsc2(Dist_Brier@data[,1]),
ggplot() +
  gg(Domain) +
  gg(Dist_Quoddy) + xlab('East(km)') + ylab('North(km)') +
  colsc2(Dist_Quoddy@data[,1]),
layout=matrix(1:4, nrow=2, ncol=2, byrow = T))

Potential repeated whale-watch and survey encounters in 2011

Could we not also put 2011’s whale-watch data into the training set? Below is some code showing that we cannot. A whale is sighted by at least one whale watch company on every day in 2011 that a survey detects a whale. The plot below shows that these encounters could have been of the same animal. Even if they weren’t, the tracklines in 2011 still visited areas that the whale watch vessels were present. Since our training and test datasets are required to be independent of each other, we must therefore also remove the 2011 whale watch encounters from the training data.

# what dates were survey encounters made on in 2011?
unique(Sightings_survey_test$DATE_LO[Sightings_survey_test$YEAR==2011])
## [1] "2011-06-21" "2011-08-12" "2011-08-13"
# Are encounters by the WW vessels made on these dates?
sum(grepl(Sightings_survey_test$DATE_LO[Sightings_survey_test$YEAR==2011][1],
     x=c(Sightings_Quoddy_nodup_test$WS_DATE[Sightings_Quoddy_nodup_test$YEAR==2011],
         Sightings_Brier_nodup_test$WS_DATE[Sightings_Brier_nodup_test$YEAR==2011])))>0
## [1] TRUE
sum(grepl(Sightings_survey_test$DATE_LO[Sightings_survey_test$YEAR==2011][2],
     x=c(Sightings_Quoddy_nodup_test$WS_DATE[Sightings_Quoddy_nodup_test$YEAR==2011],
         Sightings_Brier_nodup_test$WS_DATE[Sightings_Brier_nodup_test$YEAR==2011])))>0
## [1] TRUE
sum(grepl(Sightings_survey_test$DATE_LO[Sightings_survey_test$YEAR==2011][3],
     x=c(Sightings_Quoddy_nodup_test$WS_DATE[Sightings_Quoddy_nodup_test$YEAR==2011],
         Sightings_Brier_nodup_test$WS_DATE[Sightings_Brier_nodup_test$YEAR==2011])))>0
## [1] TRUE
# Could they be of the same animal? 
ggplot() + gg(Domain) + 
  gg(Sightings_survey_test[Sightings_survey_test$YEAR==2011,],colour='green') +
  gg.spatiallines_mod(Effort_survey_test[Effort_survey_test$YEAR==2011,],colour='yellow')

Acknowledgements

The code for hiding the Rmd code chunks came from Martin Schmelzer, found here

References to Data Sources:

References/Sources for data sets:

DFO Maritimes Region Whale Sightings Database

MacDonald, D., Emery, P., Themelis, D., Smedbol, R.K., Harris, L.E., and McCurdy, Q. 2017. Marine mammal and pelagic animal sightings (Whalesightings) database: a users guide. Can. Tech. Rep. Fish. Aquat. Sci. 3244: v + 44 p.

NOAA NARW Surveys

Timothy V.N. Cole. National Oceanic Atmospheric Administration, National Marine Fisheries Service, Northeast Fisheries Science Center. 166 Water Street, Woods Hole, MA, USA

2007 TNASS DFO Aerial Survey

Lawson. J.W., and Gosselin, J.-F. 2009. Distribution and preliminary abundance estimates for cetaceans seen during Canada’s marine megafauna survey - A component of the 2007 TNASS. DFO Can. Sci. Advis. Sec. Res. Doc. 2009/031. vi + 28 p.

NOAA Cetacean Surveys

Timothy V.N. Cole and D. Palka. National Oceanic Atmospheric Administration, National Marine Fisheries Service, Northeast Fisheries Science Center. 166 Water Street, Woods Hole, MA, USA